Grötzsch graph

triangle-free graph requiring four colors
Thing triangle_free_graph Q3115494
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Grötzsch graph

Summary

Grötzsch graph is a triangle-free graph[1]. It draws 20 Wikipedia views per month (triangle_free_graph category, ranking #1 of 1).[2]

Key Facts

  • Grötzsch graph's image is recorded as Groetzsch-graph.svg[3].
  • Grötzsch graph's instance of is recorded as triangle-free graph[4].
  • Grötzsch graph's instance of is recorded as Hamiltonian graph[5].
  • Grötzsch graph's instance of is recorded as Hamilton-connected graph[6].
  • Grötzsch graph's instance of is recorded as undirected graph[7].
  • Grötzsch graph's instance of is recorded as triconnected graph[8].
  • Grötzsch graph's instance of is recorded as Mycielski graph[9].
  • Herbert Grötzsch is named after Grötzsch graph[10].
  • Grötzsch graph's Commons category is recorded as Grötzsch graph[11].
  • Grötzsch graph's Freebase ID is recorded as /m/0268v_b[12].
  • Grötzsch graph's defining formula is recorded as -(x-1)^5 (x^2-x-10) (x^2+3 x+1)^2[13].
  • Grötzsch graph's studied by is recorded as graph theory[14].
  • Grötzsch graph's has part is recorded as node[15].
  • Grötzsch graph's has part is recorded as edge[16].
  • Grötzsch graph's MathWorld ID is recorded as GroetzschGraph[17].
  • Grötzsch graph's Wolfram Language entity code is recorded as Entity["Graph", "GroetzschGraph"][18].
  • Grötzsch graph's maintained by WikiProject is recorded as WikiProject Mathematics[19].
  • Grötzsch graph's Microsoft Academic ID is recorded as 2778413010[20].
  • Grötzsch graph's graph radius is recorded as {'amount': '+2'}[21].
  • Grötzsch graph's graph diameter is recorded as {'amount': '+2'}[22].
  • Grötzsch graph's graph girth is recorded as {'amount': '+4'}[23].
  • Grötzsch graph's The House of Graphs ID is recorded as 1132[24].
  • Grötzsch graph's Lexikon der Mathematik entry ID is recorded as 3651[25].

Why It Matters

Grötzsch graph draws 20 Wikipedia views per month (triangle_free_graph category, ranking #1 of 1).[2]

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

  1. [3] . wikidata.org.
  2. [4] . wikidata.org.
  3. [5] . wikidata.org.
  4. [6] . wikidata.org.
  5. [7] . wikidata.org.
  6. [8] . House of Graphs. wikidata.org.
  7. [9] . wikidata.org.
  8. [10] . wikidata.org.
  9. [11] . wikidata.org.
  10. [12] . wikidata.org.
  11. [13] . wikidata.org.
  12. [14] . wikidata.org.
  13. [15] . wikidata.org.
  14. [16] . wikidata.org.
  15. [17] . wikidata.org.
  16. [18] . wikidata.org.
  17. [19] . wikidata.org.
  18. [20] . wikidata.org.
  19. [21] . House of Graphs. wikidata.org.
  20. [22] . wikidata.org.
  21. [23] . wikidata.org.
  22. [24] . wikidata.org.
  23. [25] . wikidata.org.

Class ancestry

  1. [1] . Wikidata. wikidata.org.

Aggregate / graph-position facts

  1. [2] . Wikimedia Foundation. dumps.wikimedia.org.

📑 Cite this page

Use these citations when quoting this entity in research, articles, AI prompts, or wherever provenance matters. We aggregate Wikidata + Wikipedia + authoritative open-data sources; the stitched, scored, cross-referenced view is what 4ort.xyz contributes.

APA 4ort.xyz Knowledge Graph. (2026). Grötzsch graph. Retrieved May 3, 2026, from https://4ort.xyz/entity/gr-tzsch-graph
MLA “Grötzsch graph.” 4ort.xyz Knowledge Graph, 4ort.xyz, 3 May. 2026, https://4ort.xyz/entity/gr-tzsch-graph.
BibTeX @misc{4ortxyz_gr-tzsch-graph_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{Grötzsch graph}}, year = {2026}, url = {https://4ort.xyz/entity/gr-tzsch-graph}, note = {Accessed: 2026-05-03}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): Grötzsch graph — https://4ort.xyz/entity/gr-tzsch-graph (retrieved 2026-05-03)

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